The defender signed for Benfica from Barcelona in January after failing to break into the first team at the La Liga champions.
Having impressed at the Portuguese club, Jose Mourinho is targeting the signing of the Spaniard in January and United allegedly had scouts watching the 21-year-old as Benfica beat Feirense 4-0, a match in which Grimaldo scored.
United haven't had a settled left-back this season, with Luke Shaw struggling with injuries, Marcos Rojo struggling for form and Daily Blind playing a number of games at centre-back.
However, capturing the Spain U-21 international may not be easy, as Juventus and Valencia are also said to be interested in Grimaldo.